2(x2 - 4x) + 5(x + 1)x(2x + 1) - (4x - 5)(x² - 6x + 7) - (x² - 14x + 13)x(3x - 4) - 3(x² + 2) + 122x(x + 1) + x(x + 1)4(x+ - 1.5x) + 2(x? - 3)8x - 62x2 - 3x + 5Don
Answers
Starting with the first expression:
[tex]\begin{gathered} (x^2-6x+7)-(x^2-14x+13) \\ \Rightarrow x^2-6x+7+x^2+14x-13 \\ \text{collect like-terms} \\ x^2+x^2-6x+14x-13+7 \\ \Rightarrow2x^2+8x-6 \\ \\ \text{This is not the answer, as it is not the same with the two(2) expressions given in the solution} \end{gathered}[/tex]Simplifying the second expression:
[tex]\begin{gathered} 2(x^2-4x)+5(x+1) \\ \Rightarrow2x^2-8x+5x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is equal to the option B} \end{gathered}[/tex]Simplifying the third expression:
[tex]\begin{gathered} x(2x+1)-(4x-5)_{} \\ \Rightarrow2x^2+x-4x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is also equal to option B} \end{gathered}[/tex]Simplifying the fourth expression:
[tex]\begin{gathered} x(3x-4)-3(x^2+2)+12x \\ \Rightarrow3x^2-4x-3x^2-6+12x \\ \Rightarrow3x^2-3x^2-4x+12x-6 \\ \Rightarrow8x-6 \\ \\ \text{This is correct for option A} \end{gathered}[/tex]Simplifying the last expression:
[tex]\begin{gathered} x(x+1)+x(x+1)-4(x^2-1.5x)+2(x^2-3) \\ \Rightarrow x^2+x+x^2+x-4x^2+6x+2x^2-6 \\ \Rightarrow x^2+x^2-4x^2+2x^2+x+x+6x-6 \\ \Rightarrow8x-6 \\ \\ \text{This expression is also true for option A} \end{gathered}[/tex]Related Questions
An initial amount of radioactive substance Y0is given, along with information about
the amount remaining after a given time t in appropriate units. For an equation of
the form y=yoekt that models the situation, give the exact value of k.
Y0=10 mg, the half-life is 100 days
Answers
The value of k in this exponential decaying situation of radioactive material is - 0.0069.
What is an exponential function?One of the key mathematical operations is the exponential function we allow the exponent to be the independent variable to create an exponential function.
Given, An equation of the form y = y₀e^(kt) models a situation of decaying radioactive material.
y₀ = 10mg, half-life = 100 days.
So, in 100 days the left-out radioactive material will be 5mg.
∴ 5 = 10.e^(100k).
e^(100k) = 1/2.
lne^(100k) = ln(1/2).
100k = - 0.69
k = - 0.69/100.
k = - 0.0069.
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can someone please help me i don't understand this
Answers
Answer:
Step-by-step explanation:
equation of finding a midpoint is (x2+x1)/2 and (y1+y2)/2
7) (4+12)/2 = 8 and (9+-4)/2= 2.5
hence midpoint is (8,2.5)
8) we are told the midpoint so we can now find the co-ordinates of the other endpoint:
(5+x)/2= -3
rearrange to find x--> 5+x =-6, so x=-11
(-7+y)/2=2
rearrange to find y--> -7+y=4, so y=11
other endpoint: (-11,11)
5) the gradient of the new equation is parallel to y=3x+7 so it will stay the same
y=3x+c
we know that the points this line passes through is: (-4,-8) so we substitute this into our new equation to find c
-8= (3 x -4) +c
-8=-12 +c
so c= 4
Hence our new equation is y=3x+4
6) perpendicular gradient means that our existing gradient needs to be reciprocated (turned into negative and then flipped)
new gradient is -1/3
y=-1/3x+c
we know the value for x and y so we can substitute into our new equation to find c
9=(-1/3 x -6) +c
9=2 + c
c= 7
Hence our new equation is y=-1/3x+7
Hope this helps!
The radius of a cylindrical water tank is 6.5 ft, and its height is 12 ft. What is the volume of the tank? Use the value 3.14 for T, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer. Continue 6.5 ft 12 ft 0 K ft X ft² 5 ft3 ?
Answers
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} volume=\pi r^2h \\ where \\ r\Rightarrow radius\text{ of its circular end} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylindrical water tank below:
where
[tex]\begin{gathered} r=6.5\text{ ft} \\ h=12\text{ ft} \\ \pi=3.14 \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} volume\text{ = 3.14}\times(6.5)^2\times12 \\ =1591.98 \\ \Rightarrow volume\approx1592\text{ ft}^3\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the volume of the cylindrical water tank, to the nearest whole number, is
[tex]1592\text{ ft}^3[/tex]Write an equation of a parabola that opens upward, has a vertex at the origin, and a focus at (0, 1).
Answers
The focus of a parabola does not lie on it. Hence, the equation of parabola is given as y² = 2y - x².
What is a parabola?The parabola can be defined as a conic section curve, all of whose points are equidistant from a fixed point called as focus and a fixed line called as directrix.
Given that,
The focus of parabola is (0, 1).
The vertex of parabola is (0, 0).
Suppose, there is one more point on parabola as (x, y).
Since focus of a parabola is equidistant from all the points on parabola.
Use distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) as √((x₂ - x₁)² + (y₂ - y₁)²) to find the equation of parabola as,
√((x - 0)² + (y - 1)²) = √((0- 0)² + (0 - 1)²)
=> x² + (y - 1)² = 1
=> (y - 1)² = 1 - x²
=> y² - 2y + 1 = 1 - x²
=> y² = 2y - x²
Hence, the equation of the parabola having vertex at origin and focus at (0, 1) is y² = 2y - x².
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What is the product of (−7)(14) • (−6)? 92 −77 588 −104
Answers
The product of (− 7) ( 14 ) multiplied by ( −6 ) will be C. 588.
What is a product?A product simply means the value that's gotten when the numbers are multiplied together. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that minus × minus = plus
minus × plus = minus
Therefore, the value of ( −7 ) ( 14 ) • ( −6 ) will be:
= ( -7 ) × 14 × ( -6 )
= 588
Therefore, the value of the product is 588 and this implies that the correct option is C.
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Which of the following is a factor of x³ + 343?
x-7
x² - 14x + 49
x² + 7x +49
x+7
Answers
Answer:factor of x³ + 343
Step-by-step explanation: Option D is correct. A factor of an expression is usually referred to as a number or an algebraic expression that divides the known expression. The above algebraic expression needs to be expanded to determine its factor; Mathematically; x³ + 343 = (x + 7) (x² - 7x + 49) Therefore, we can conclude that the factors are (x + 7) (x² - 7x + 49)
[{12 - 6 (5 - 3) + 2} + 5 (6-71]
Answers
Here, we want to evaluate the expression
We use the order of operations here PEDMAS ( parentheses, exponents (roots and powers) , division, multiplication, addition and subtraction)
We start out with the parentheses, then move on with the terms outside by multiplication
We have this as follows;
[tex]\begin{gathered} ((12\text{ -6(2)+2)) + 5(-65))} \\ =\text{ ((12-12+2)-325)} \\ =\text{ 2-325 = -323} \end{gathered}[/tex]the diagram shows a sector of a circle, center O. The radius of the circle is 6cm. angle AOB is 120. work about the perimeter of the sector.
picture below:
Answers
The perimeter of the sector is 2cm
The diagram shows a sector of a circle, center O.
The radius of the circle is 6cm.
The angle AOB is 120
We need to find the perimeter of the sector
s = r∅
Where ∅ is the angle subtended by the arc
r is the radius of the circle
s = 6 (120/360)
s = 6 (1/3)
s = 2
Therefore, the perimeter of the sector is 2cm
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What are the factors of the following quadratic?x2 + 9x + 8
Answers
we have
x2 + 9x + 8
Find the factors
Complete the square
(x^2+9x+81/4)-81/4+8=0
Rewrite as perfect squares
(x+9/2)^2=81/4-8
(x+9/2)^2=49/4
square root both sides
(x+9/2)=(+/-)7/2
x=-9/2(+/-)7/2
so
x1=-9/2+7/2=-1
x2=-9/2-7/2=-8
therefore
x2 + 9x + 8=(x+1)(x+8)
answer is
The factors are
(x+1) and (x+8)
Which of the following ratios are equivalent to 8:2?
A 16:4
B 40:10
C 2:8
D 10:4
E 1:6
F 4:1
Answers
8 • 2 = 16
2 • 2 = 4
Answer:
A, B, F
Step-by-step explanation:
Well, to do this let's start by simplifying each of the ratios! If they can be simplified to 8:2 then they are a match
A: 16:4
Divide both sides by 2: 8:2 (This is an answer)
B: 40:10
Divide both sides by 5: 8:2 (This is also an answer)
C: 2:8
This one is not possible, because you would have to multiply the 2 by a whole number, and the 8 by a number less than one. Both have to be multiplied/divided by the same number.
D: 10:4
To get the 4 into a 2, we divide by 2. If we divide the 10 by 2 we get 5. Thus, this is not an answer.
E: 1:6
To get the 6 into a 2, we must divide it by 3. If we divide 1 by 3, we get a decimal, not 8.
F: 4:1
Multiply both sides by 2: 8:2 (This is our final answer)
The piston diameter of a certain hand pump is inch. The manager determines that the diameters are normally distributed, with a mean of inch and a standard deviation of inch. After recalibrating the production machine, the manager randomly selects pistons and determines that the standard deviation is inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the level of significance?.
Answers
We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01
What is standard deviation?
The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.
The null and alternative hypotheses are:
[tex]H_{0} :[/tex] α = 0.004
[tex]H_{a} :[/tex] α < 0.004
Under null hypothesis, the test statistic is:
[tex]x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }[/tex]
= (29 - 1)0.0036² / 0.004²
= 22.68
Now the critical value of x² at 0.01 level of significance for
df = n-1
= 29 - 1
= 28
[tex]x_{critical} ^{2}[/tex] = 48.278
Since the test statics
x² = 22.68 is less than the critical value
[tex]x_{critical} ^{2}[/tex] = 48.278
∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01
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HELPPPP PLSSSS I NEED A STEP BY STEP
Answers
Answer:
see explanation
Step-by-step explanation:
If the ratios of two pairs of corresponding sides of the 2 triangles are equal and the included angles are congruent then the triangles are similar by the
SAS postulate.
[tex]\frac{AC}{DF}[/tex] = [tex]\frac{5.1}{1.7}[/tex] = 3
[tex]\frac{BC}{EF}[/tex] = [tex]\frac{3.3}{1.1}[/tex] = 3
∠ C = 180° - (36 + 67)° = 180° - 103° = 77° , then the included angles
∠ C and ∠ F = 77° are congruent
Then
Δ ABC and Δ DEF are similar by the SAS postulate
select the correct location on the graph PICTURE OF PROBLEM AND GRAPH BELOW
Answers
Given the graphed equation:
[tex]0.01x^3-3=|x|-5[/tex]Let's determine the point that represents a negative solution for x.
The solutions are the points where both lines meet.
From the graph, the solution which has a negative solution for x is:
(-2, -3)
In this point of intersection, the value of the x-coordinate is -3 (which is a negative value).
Therefore, the point which represents a negative solution for x is:
(-2, -3)
ANSWER:
(-2, -3)
what is the perimeter, in meters, of a rectangular garden 6 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
Answers
The perimeter of the Garden is 76 meters. and the length is 32m.
Area= L × B
(L×6) = 16 × 12
L = [tex]\frac{288}{6}[/tex] = 32m
Therefore L works out to 32 meters.
Perimeter of Garden = 2 × (32+6) = 76 meter.
The area is the quantity that expresses the extent of a place on the plane or on a curved floor. The area of an aircraft area or aircraft location refers to the region of a shape or planar lamina, at the same time as floor vicinity refers back to the region of an open surface or the boundary of a three-dimensional object. the vicinity may be understood as the quantity of cloth with a given thickness that would be essential to fashion a version of the form, or the amount of paint necessary to cover the floor with an unmarried coat. it's miles the two-dimensional analog of the period of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
vicinity of a form may be measured by evaluating the form to squares of a fixed size. inside the international system of devices (SI), the usual unit of the region is the rectangular meter (written as m²), which is the region of a square whose facets are one meter lengthy. A shape with a place of three square meters would have the same place as 3 such squares. In arithmetic, the unit rectangular is defined to have region one, and the place of any other shape or floor is a dimensionless actual wide variety.
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Which equation represents the total commission (c) a sales associate receives if he sells laptop computers (l) with a commission of $39.95 for each sold laptop? What's the total commission if he sells 15 laptops?
A)
l = 39.95c; $599.25
B)
c = 39.95l; $2.66
C)
l = 39.95c; $2.66
D)
c = 39.95l; $599.25
Answers
Answer:
D
Step-by-step explanation:
The total commission is the number of laptops times the commission per laptop. Thus, [tex]c=39.95l[/tex].
Setting [tex]l=15[/tex], [tex]c=39.95(15)=599.25[/tex].
.A jar contains 15 green marbles numbered 1 through 15 and 9 red marbles numbered 1 through 9. A marble isdrawn at random from the jar. Find the probability that the marble is green or even numbered.
Answers
Answer: 19/24
Explanation:
From the information given,
Number of green marbles = 15
Number of red marbles = 9
Total number of marbles = 15 + 9 = 24
Probability is expressed as
number of favorable outcomes/number of total outcomes
Probability f selecting a greeen marble = 15/24
Even numbers divide 2 without a remainder. The even numbered marbles are
red = 2, 4, 6, 8
green = 2, 4, , 68, 10, 12, 14
Total number of even numbered marbles = 11
Probability of selecing an oevennumber = 10124
The events are not mutually exclusive becuse they can occur together. For two ebvents, A and B that are not mutually exclusive,
P(A U B) = P(A) + P(B) - P(A and B)
Thus,
the probability that the marble is green or even numbered = Probability of selecting a green marble + Probability of selecting an even number - Probability of selecting a green and even numbered marble
Number of green even numbere marble s = 7
Probability of selecting a green and even numbered marble = 7/24
Thus,
the probability that the marble is green or even numbered = 15/24 + 11/24 - 7/24
the probability that the marble is green or even numbered = 19/24
identify the term in experimentation -2X
Answers
The given expression is
[tex]-2x^8+3x^2-x+11[/tex]Terms are the expressions separated by negative or positive signs. In this case, there are 4 terms.
Coefficients are the number multiplying the variable. IN this case, the coefficients are -2, 3, and -1.
The variable is just x because it's the only letter present in the expression.
The powers are x'8 and x'2.
Finding the final amount in a world power problem on a compound interest
Answers
Using the compound interest formula, we have:
[tex]FV=2000(1+\frac{0.12}{2})^{6\cdot2}[/tex][tex]FV=2000(1.06)^{12}[/tex][tex]FV\approx4024.39[/tex]How many deciliters are in 1 milliliter?100100.10.01
Answers
We are asked to find how many deciliters can be found in 1 mililiter.
To get the solution we have to find the conversion factor. All we need to do is divide the volume by 100.
Here is a formula
[tex]\text{Value in deciliters =}\frac{Value\text{ in mililiters}}{100}[/tex]This implies,
[tex]\begin{gathered} \text{Value in deciliters=}\frac{1}{100} \\ \text{Value in deciliters}=0.01 \end{gathered}[/tex]ANSWER: 0.01
Factor the expression 36a + 42b - 18a + 6
+10 points=brainliest
Answers
Answer:
6(3a+7b+1)
Step-by-step explanation:
36a+42v-18a+6
18a+42b+6
GCF=6
6(3a+7b+1)
The factor of the given expression is 6(3a+7b+1).
What are factors?A factor is a number that divides another number, leaving no remainder.
Given an expression, 36a + 42b - 18a + 6
On factoring, we get,
36a + 42b - 18a + 6
= 18a+42b+6
= 6(3a+7b+1)
Hence, The factor of the given expression is 6(3a+7b+1).
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In a college there are 16 times as many students as professors. If together the students and professors number 42,500, how many students are there in the collego?The number of students in the college is
Answers
Let the number of professors be x.
If there are 16 times as many students as professors, then the number of students will be:
[tex]x\times16=16x[/tex]If the number of students and professors is 42,500, then we have that:
[tex]\begin{gathered} x+16x=42500 \\ 17x=42500 \end{gathered}[/tex]Solving by dividing both sides by 17, we have:
[tex]\begin{gathered} x=\frac{42500}{17} \\ x=2500 \end{gathered}[/tex]Hence, we can calculate the number of students in the college to be:
[tex]\Rightarrow2500\times16=40000[/tex]Therefore, there are 40,000 students in the college.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 8in by 2 3/4 by 2 3/4.If the bricks cost $0.06 per cubic inch, find the cost of 850 bricks. Round your answer to the nearest cent.
Answers
Given the building that can be modeled as a
right rectangular prism with dimentions
8 * 2 3/4 * 2 3/4
Volume is given by
[tex]V=8*2\frac{3}{4}*2\frac{3}{4}[/tex][tex]V=8*2\frac{3}{4}*2\frac{3}{4}[/tex][tex]V=60.5in^3[/tex]since we have 850 bricks
the volume occupied by 850 bricks is therefore
[tex]Vbricks=60.5*850[/tex][tex]Vbricks=60.5*850[/tex][tex]Vbricks=51425[/tex]then
the cost of the 850 bricks is
[tex]Cbricks=51425*0.06[/tex][tex]Cbricks=3085.5[/tex]cost of bricks is $3085.50
Simplify: 3 3/9+2 10/18
Answers
The answer of the given fraction after simplification is 2.11.
Define simplification.To simplify simply means to make anything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given fraction is:
= 3 * 3/9 + 2 * 10/18
By simplifying the given fraction, we get
= 3 * 1/3 + 10/9
= 1 + 1.11
= 2.11
The answer of the given fraction after simplification is 2.11.
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Find an equation for the line below.A(-6, -3) B(2,-5)
Answers
Using Two point formula in getting the equation of the line.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]x1 = -6
y1 = -3
x2 = 2
y2 = -5
Substitute to the formula :
[tex]\begin{gathered} y-(-3)=\frac{-5-(-3)}{2-(-6)}\lbrack x-(-6)\rbrack \\ y+3=\frac{-2}{8}(x+6) \\ y+3=-\frac{1}{4}(x+6) \\ y+3=-\frac{1}{4}x-\frac{3}{2} \\ y=-\frac{1}{4}x-\frac{3}{2}-3 \\ y=-\frac{1}{4}x-\frac{9}{2} \end{gathered}[/tex]The answer is :
y = -1/4 x - 9/2
How to calculate the volume of this shape?
(1 litre = 1000 cm^3)
Answers
Answer:
it is half of volume of tube.
tube volume = area of circle (πr)× height of tube (h)
volume of tube = π × r × t
1/2 tube volume = 1/2 × π × r × h
PLS HELP ILL MATK BRAINLIEST
the area of a square garden is
84 square
feet what is the best estimate of the sidelenght of the garden
21
11
7
9
Answers
Answer:
40q7572928254949262618394938282920420
y 'varies inversely with x.
If x = 6 and y = 5, find y when x = 3
Answers
Answer: y = 2
Good luck!
9.3 divided by 3.8 HELP ME
Answers
Answer:
Step-by-step explanation:
0 0. 4 0
9 3 3 8. 0 0
− 0
3 8
− 0
3 8 0
− 3 7 2
8 0
− 0
8 0
0.40
2.45 is the answer to 9.3 divided by 3.8
Divide £350 in the ratio
3:11
Answers
£350 is divided in the ratio 3:11 is £75 and £275.
The given ratio is 3:11.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
We need to divide £350 in the given ratio
Now, 3+11=14
3/14 × 350
= £75
11/14 × 350
= £275
Hence, £350 is divided in the ratio 3:11 is £75 and £275.
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